Dea Efficiency Evaluation Of The Decision-making Unit Containing Multiple Subsystems

Efficiency evaluation is regarded as a task of high frequency, great difficulty and remarkable importance in economic circles, or in social activities. The conception efficiency mentioned in this paper is technical efficiency, which originated from the economical field. In 1957 Farrell first proposed to employ Frontier Production Function to estimate technical efficiency, and he defined technical efficiency as the ratio of the actual production competence and the frontier production competence. The paper extends this viewpoint to any type of systems with inputs and outputs, such as finance, public sector and sports, not limited to manufacturing enterprises.Basically this paper employs Data Envelopment Analysis (DEA) to gauge technical efficiency. DEA is a resultful tool to evaluate the relative efficiencies among Decision Making Units (DMUs) with multiple inputs and multiple outputs. Charnes et al set up the first DEA model, i.e. CCR model, in 1978. Henceforth DEA become one of the most important methods for efficiency evaluation.The traditional DEA models regard DMUs as black boxes and ignore the internal structure of DMUs. In fact this method is based on the assumption that the internal operations are efficient and overrate the system input-output efficiency consequentially. The major goals of this paper include: (1) DMU classification; (2) developing DEA models for each classification of DMUs. Then DEA models can be applied to a large majority of operations with complex internal structures.The objects of this paper are DMUs with multiple subsystems, and DMUs are called systems concluding a group of homogeneous operations, or different observations of the same operation. In a system or a DMU, the subsystems exhibit in the structure of chains, trees, annularities, networks or discrete states. So the paper principally includes 5 chapters: (1) efficiency evaluation to chain-like systems; (2) efficiency evaluation to parallel systems; (3) efficiency evaluation to tree-like systems; (4) efficiency evaluation to annularity-like systems; (5) efficiency evaluation to network systems.In Chapter 2, this paper studies how to appraise a chain-like system's DEA efficiency, and discusses the relations of subsystem performances and system performance, and relevancies among subsystem efficiencies. Chapter 2.2 indicates that the status discrepancy of subsystems will influence the decision of correlative weigh variables and the optimal values of DMU efficiencies. Chapter 2.3 shows that there exists an efficiency game between the two subsystems based on the two efficiency functions in the decentralized control mechanism. According to Farrell theory, Chapter 2.4 tables a proposal to appraise a chain-like system's DEA efficiency. Besides, this chapter also develops a means to estimate the Frontier Production Functions of chain-like systemsIn Chapter 3, this paper studies how to appraise a parallel system's DEA efficiency. In this chapter the author reviews some accomplishments about parallel system efficiency evaluation, advances a new method, and proofs the equivalence of the means mentioned above.